Determination of the Radioisotope Decay Constants and Half-li es: Potassium-40 ( 40 K)

Transcription

1 9 (2016): Determination of the Radioisotope Decay Constants and Half-lies: Potassium- ( K) Andrew A. Snelling, Answers in Genesis, PO Box 510, Hebron, Kentucky, Abstract Over the last 78 years numerous determinations have been made of the total K decay half-life, obtained by direct counting experiments and by comparing radioisotope ages derived from more than one dating method applied to the same rocks or minerals. The determinations since 1997 have converged with close agreement toward the total K decay half-life value of ± Byr. But that determination in 2011 ignored the two liquid scintillation direct counting determinations in 2002 and 2004 which had agreed on a slightly lower total K decay half-life value of ± Byr. So neither of these values has yet been adopted for standard use by the uniformitarian geochronology community. There are important sources of systematic error in all Ar- Ar (and K-Ar) ages that arise from uncertainties in the two K decay constants and determination of the total K decay half-life, the branching ratio between Ca and electron capture decay to ± determined in The uncertainties in the crucial K/K abundance ratio also need to be considered, because there is no agreement on it. The value of ± % determined in 1975 is still adopted, but the value of ± % determined in 2013 has yet to be recognized. Therefore, when all these factors are considered the total K decay half-life is thus known to no better than ± 2% at the Ar*/ K ratios for individual standards are only known to better than ± 2% in some cases, while interlaboratory discrepancies of more than 2% in the Ar/ Ar ages of secondary standards like the Fish Canyon Tuff sanidine suggest larger uncertainties. Thus independent determinations of the branching and K/K abundance ratios are still needed, as well as new laboratory investigations to determine the total K decay half-life. Yet, in spite of the many experiments directly measuring the total K decay half-life, the adopted value ultimately depends on deriving it by adjusting (that is, massaging) K-Ar and Ar-Ar ages to conform to U-Pb and Pb-Pb ages obtained from different minerals respectively in the same rocks. But many unprovable assumptions are also involved, not the least being that the radioisotope systems closed at the same time and subsequently remained closed. Furthermore, even this U-Pb gold standard has unresolved uncertainties due to the U decay constants being imprecisely known, and to measured variations of the 238 U/ 235 U ratio in terrestrial rocks, ores, and minerals, and in meteorites. Both of these factors are so critical to the U-Pb method, as well as the additional factor of knowing the initial concentrations of the daughter and index isotopes, so it should not be used as a standard to determine other decay constants. There is also evidence decay rates of the radioisotopes used for rock dating have not been constant in the past, as well as the possibility of a slight decline in the measured values of the total K decay half-life during the 78 years of determinations. This only serves to emphasize that if the K-Ar and Ar-Ar dating methods have been calibrated against the U-Pb gold standard with all its attendant uncertainties, then they cannot be absolute, and therefore they cannot be used to reject the young-earth creationist timescale. Indeed, current radioisotope dating methodologies are at best hypotheses based on extrapolating current measurements and observations back into an assumed deep time history for the cosmos. Keywords: radioisotope dating, decay constants, half-lives, potassium-, experiments, Geiger-Müller counter, liquid scintillation counter, geological comparisons, Fish Canyon Tuff sanidine, uncertainties, branching ratio, K/K abundance ratio, U-Pb gold standard, 238 U/ 235 U Introduction Radioisotope dating of rocks and meteorites is perhaps the most potent claimed proof for the supposed old age of the earth and the solar system. The absolute ages provided by the radioisotope dating methods provide an apparent aura of certainty to the claimed millions and billions of years for formation community and the general public around the world thus remain convinced of the earth s claimed great antiquity. However, accurate radioisotopic age determinations require that the decay constants (or half-lives) of the respective parent radionuclides be accurately known and constant in time. Ideally, the uncertainty of the decay constants should be negligible compared to, or at least be commensurate with, the analytical uncertainties of the mass spectrometer measurements entering the radioisotope age calculations (Begemann et al. 2001). Clearly, based on the ongoing discussion in the conventional literature this is still not the case at present. The ISSN: Copyright 2016 Answers in Genesis, Inc. All content is owned by Answers in Genesis ( AiG ) unless otherwise indicated. AiG consents to unlimited copying and distribution of print copies of Answers Research Journal articles for non-commercial, non-sale purposes only, provided the following conditions are met: the author of the article is clearly identified; Answers in Genesis is acknowledged as the copyright owner; Answers Research Journal and its website, are acknowledged as the publication source; and the integrity of the work is not compromised in any way. For website and other electronic distribution and publication, AiG consents to republication of article abstracts with direct links to the full papers on the ARJ website. All rights reserved. For more information write to: Answers in Genesis, PO Box 510, Hebron, KY 41048, Attn: Editor, Answers Research Journal. The views expressed are those of the writer(s) and not necessarily those of the Answers Research Journal Editor or of Answers in Genesis.

2 172 A. A. Snelling stunning improvements in the performance of mass spectrometers during the past four or so decades, starting with the landmark paper by Wasserburg et al. (1969), have not been accompanied by any comparable improvement in the accuracy of the Jäger 1977), in spite of ongoing attempts (Miller 2012). The uncertainties associated with direct halflife determinations are, in most cases, still at the radioisotope method for determining the ages of rock formations. However, even uncertainties of only 1% in the derived radioisotope ages. The recognition of an urgent need to improve the situation is not new It continues to be mentioned, at one time or another, by every group active in geo- or cosmochronology (Schmitz 2012). Radioisotopes and the Age of The arth) project successfully made progress in documenting some of the pitfalls in the radioisotope dating methods, and especially in demonstrating that radioisotope decay rates may not have always been constant at today s measured rates (Vardiman, effort remains to be done to make further inroads long-age dating methods, but towards a thorough understanding of radioisotopes and their decay during the earth s history within a biblical creationist framework. on was the issue of how reliable have been the determinations of the radioisotope decay rates, which are so crucial for calibrating these dating clocks. Indeed, before this present series of papers attempts in the creationist literature to review how the half-lives of the parent radioisotopes used in longage geological dating have been determined and to collate all the determinations of them reported in the literature to discuss the accuracy of their currently accepted values. After all, accurate radioisotope age determinations depend on accurate determinations of the decay constants or half-lives of the respective parent radioisotopes. The reliability of the other two assumptions these supposed absolute dating methods rely on, that is, the starting conditions and no contamination of closed systems, are unprovable. via the isochron technique, because it is claimed to be independent of the starting conditions and is claimed to be sensitive to revealing any contamination, which method for determining the ages of rock formations. ignored because their values are regarded as due to contamination. That this is common practice is is arbitrary and therefore is not good science, because it is merely assumed the aberrant values are due to contamination rather than that being proven to be so. Indeed, in order to discard such outliers in any data set, one must establish a reason for discarding those data points which cannot be reasonably questioned. documented the methodology behind and history of determining the decay constants and half-lives of the parent radioisotopes Rb, 176 Lu, Re, and Sm which are used as the basis for the Rb-Sr, Lu-Hf, respectively. He showed that there is still some uncertainty in what the values for these measures of the Rb and 176 Lu decay rates should be, in contrast to the apparent agreement on the Re and Sm decay rates. This uncertainty is especially prominent in determinations of the 176 Lu decay rate by physical direct values of the Rb decay rate differ when Rb-Sr ages terrestrial minerals and rocks or the same meteorites and lunar rocks. Ironically it is the slow decay rates of isotopes such as Rb and Sm used for deep time dating that makes precise measurements of their direct measurements of their decay rates should be because measurements which are calibrated against other radioisotope systems are already biased by the currently accepted methodology employed by the secular community in their rock dating methods. Rb, 176 Lu, Re, and Sm decay half-lives radioisotope systems. This is the case even for the Sm decay half-life whose accepted value has not changed meteorites in the 1970s, in spite of the fact that more radioisotope dating as the gold standard is very questionable, as there are now known measured variations in the U/ 235 U ratio that is critical to that 2012), as well as uncertainties as to the U and 235 U

3 173 Therefore, the aim of this contribution is to further document the methodology behind and history of determining the present decay constants and half-lives of the parent radioisotopes used as the basis for the long-age dating methods. We need are, whether there really is consensus on standard values for the half-lives and decay constants, and just how independent, consistent, and objective the standard values are for each of the different methods. radioactive isotope is likely to show similar variation and uncertainty in half-life measurements because concomitant high statistical errors. This would also apply to determination of the amount of daughter isotope produced via the decay process. However, even small variations and uncertainties in the halflife values result in large variations and uncertainties in the calculated ages for rocks, and the question remains as to whether the half-life values for each long-lived parent radioisotope are independently determined. We continue here with determinations Potassium, Potassium- Decay and Potassium-Argon Dating Z=19) is an alkali metal (group IA), along with Li, Na, Rb, and Cs. It is one of the eight most abundant chemical elements in the earth s crust and is a major constituent of many important rockforming minerals, such as the micas, the feldspars, the feldspathoids, many clay minerals, and some and Mensing 2005). by Aston (1921), who discovered (1905) and was subsequently demonstrated by However, the naturally-occurring radioisotope more sensitive mass spectrometer than had been available to Aston. The possible modes of decay open to who concluded that to Ca and to Ar, based partly on the fact that the abundance of Ar in the earth s atmosphere is about the cosmic abundances of the other noble gases. Von Weizsäcker (1937) also postulated that radiogenic Ar demonstrating that four geologically old minerals did contain radiogenic Ar. The theoretical basis for and since then it has become an important and isotopes whose abundances have been determined as and thus effectively falls in the low-ppm concentration range in rocks and minerals. The isotopic composition of Ar in the terrestrial atmosphere was measured by Nier (1950) as Ar = 99.60%, Ar = 0.063%, and 36 Ar = 0.337%, so that the Ar/ 36 Ar ratio is 99.60/0.337 = Naturally-occurring scheme to Ca and Energy, MeV Branched Decay of K 19 Ar 18 Ar 18 e.c MeV e.c. = MeV K Atomic Number Ca 20 Fig. 1. Ar and Ca (after Ar proceeds by means of electron capture (e.c.) and positron decay. been combined in this diagram with the energy of the emission leads to the ground state of Ca. The energetic properties of electron capture mode. (Data from Dalrymple and Negatron = MeV

4 174 A. A. Snelling to Ca, but in most rocks the Ca daughter product is swamped by common (non-radiogenic) Ca, which Ar, but by three different routes, two of which involve capture two electron capture modes leaves the Ar nucleus Mensing 2005). The second electron capture mode and the positron decay both reach the ground state of Ar directly. However, the third route by positron emission makes up only 0.001% of decays to Ar. Therefore, the electron capture (etc.) decay constant can be taken to represent all of the routes from Ar (Dickin 2005). ec has -10 per year, equivalent to a half-life of Byr (Steiger and best counting determinations at the time evaluated which has to also be taken into account. It has a recommended -10 per year, equivalent to a halflife of 1.7 Byr (Steiger and Jäger 1977). Thus the for -10 per year, equivalent to a half-life of 1.25 Byr (Steiger and Jäger 1977). As already indicated, there are two parameters t ½ ). per unit time of a particular nucleus decaying, whereas the half-life is the time it takes for half of a given number of the parent radionuclide atoms to decay. The two quantities can be almost used interchangeably, because they are related by the equation:- ln t 12 (1) The branching ratio R ec and has a of ec Ar atoms ( Ar* K(e 1) ec t The total number of Ar atoms is: Ar= Ar + Ar* 0 (2) (3) where Ar 0 is the number of Ar atoms per unit weight of sample that were incorporated into the rock or mineral at the time of its formation. Since Ar is a noble (or inert) gas and since its solubility in silicate melts is thus low, Ar 0 is assumed to be zero. It could be argued that this is a questionable assumption to verify, especially since only a relatively small amount of Ar is incorporated into the rock via radioactive decay. method, the number of Ar* atoms in a unit weight of sample must be measured and then used to solve equation 2 for t: 1 Ar* t= ln +1 K ec the value of t so calculated is the age (that is, the model age) of the rock or mineral only when the 1. No radiogenic Ar* produced by decay of rock or mineral during its lifetime has escaped. 2. The rock or mineral became closed to Ar soon after its formation, which means it must have cooled rapidly after crystallization, unless it formed at a low temperature. 3. No Ar was incorporated into the rock or mineral either at the time of its formation or during a later metamorphic event. An appropriate correction is made for the presence of atmospheric Ar. 5. lifetime. 6. is normal and was not changed by fractionation or 7. The decay constants (or half-lives) of known accurately and have not been affected by the physical or chemical conditions of the was incorporated into the earth. Ar* were determined accurately. assumptions require careful evaluation in each case and place certain restrictions on the geological and Ar-Ar dates have been obtained for various rocks and minerals due to the demonstrated failure of some of these assumptions. The last three assumptions fundamental conditions of any radioisotope dating

5 175 samples is usually regarded as constant, even though small scale across contacts of igneous intrusions Schreiner 1967). However, if the total of any rock or mineral cannot be known accurately either. These problems led to the development of the argon-argon (Ar-Ar) dating method. Argon-Argon Dating In addition, the decay of Ar is also the basis for the Ar- Ar dating method, which uses an unconventional approach to the problem of on the assumptions that the sample contained no Ar at the time of its formation and all the radiogenic Ar produced within it was quantitatively retained out of minerals even at temperatures well below their the time elapsed since cooling to temperatures at Ar be too old. That this is a common problem has been the concentrations of separately on different aliquots of the samples, unknown systematic errors. Therefore, the samples being dated must be homogeneous with respect to both elements. But this requirement may not be glassy volcanic rocks. Ar*- described in detail by Merrihue and Turner (1966). This method can overcome some of the limitations only measurements of the isotope ratios of Ar are required. The problem of inhomogeneity of samples and Ar are thus eliminated. This method is therefore claimed to be well suited to the dating of small or valuable samples such as meteorites or lunar rocks and minerals, especially when samples are heated stepwise with a continuous laser. The Ar- Ar dating method is based on the formation of Ar by converting samples to Ar in a nuclear reactor by irradiation with thermal and fast neutrons. This causes the desired n, p (neutron capture, proton emission) reaction: K n Ar p Ar is unstable and decays to with a half-life of 269 years. Because of its slow decay rate (comparatively long half-life), Ar can be treated as though it were stable during the short time involved in the analyses of samples. Merrihue Ar*/ Ar ratio could be measured by mass spectrometry. Subsequently Merrihue and Turner (1966) described such a procedure and reported the Ar-Ar dates for several stony meteorites that appeared to be in the same meteorites. The principles of the Ar- Ar dating method have been presented by Dallmeyer (1979), Dalrymple and Lanphere (1971), Dalrymple neutrons in a reactor, isotopes of Ar are produced target. In the ideal case, Ar is produced only by the n, p reaction with Ar atoms formed in the sample by the neutron irradiation is A K T ( ) ( )d where T is the duration of the ) is the capture cross-section of having energy, and the integration is carried out over the entire energy spectrum of the neutrons. The number of radiogenic Ar atoms in the irradiated sample due to decay of by equation 2 above, where Ar* is the radiogenic ec is the decay constant of neutron irradiation of a sample, its Ar*/ Ar ratio is obtained by dividing equation 2 above by equation 6 Ar * t K( e 1) d ec Ar K T ( ) ( ) the energy spectrum of the incident neutrons and the cross-sections of energies are not well known. So equation 7 can be J (5) (6) (7)

6 176 A. A. Snelling K ec J= T () () d K which leads to t Ar* e 1 (9) Ar J J might be determined by irradiating samples of known age (which are called whose ages are unknown and are being determined. being measured, but it is the Ar*/ Ar ratio that is really being measured by this methodology. So after the Ar*/ Ar ratio of the monitor has been measured, J can be calculated from equation 9 ( t m e 1) J Ar * (10) Ar m where t m is the known age ( Ar*/ Ar) m is the measured value of this ratio in the inserted into the sample holder at known positions between unknown samples. The entire package is then irradiated for several days in a nuclear reactor to allow Ar to be produced. This of course assumes a known age) is released by fusion in a vacuum system and their Ar*/ Ar ratios are measured by mass spectrometry. It is assumed that all the Ar, with no fractionation occurring, is released from the monitors and collected for mass spectrometry analyses. Their J values are then calculated using equation 9 and are plotted as a function of their position in the sample holder. The respective J values of the unknown age samples are then obtained by interpolation of the resulting graph according to their known positions in the sample holder. It is only possible to apply these J values to the samples of unknown ages because both those samples and the monitors were irradiated at the same time. The Ar*/ Ar ratios of the irradiated unknown age samples are determined similarly by melting them individually in a vacuum chamber and by measuring the Ar*/ Ar ratio of the released Ar in a gas source mass spectrometer. The resulting Ar*/ Ar ratios of the unknown age samples are then used to calculate their ages using equation 9 rearranged as 1 Ar* t ln 1 Ar J (11) Several different mineral concentrates have been used as monitors. Their ages must be accurately known because they are used for calculating values of J using equation 10. Any errors in the ages of the monitors are therefore propagated from equations 10 and 11 and result in corresponding systematic errors in the calculated Ar*/ Ar ages of the samples of 2010), Schwartz and Trieloff (2007a), and Roddick determine the Ar-Ar ages of the samples of unknown ages still involves circular reasoning. The estimated analytical error in the calculated age using equation 11 according to Dalrymple and Lanphere (1971) is 1 2 JF 2 2 ( 2 2 F j t (12) t (1 FJ) where F = Ar*/ 2 2 Ar, F and j are the variances of F and Jt is the of are subject to the same limitations as conventional that no radiogenic Ar has escaped from the samples Ar is present. However, such ages avoid the problems arising from the inhomogeneous the measurements of isotope ratios of Ar. In the ideal case outlined above it is assumed that all of the Ar in the irradiated samples is either radiogenic or atmospheric, all of the 36 Ar is atmospheric, and the Ar is produced only by the Ar reaction during the irradiation process. In this case the measured values of the Ar/ Ar and 36 Ar/ Ar ratios can be used to calculate the desired ratio of radiogenic Ar ( Ar*) to Ar by the relationship 36 Ar * Ar Ar (13) Ar Ar Ar where is the Ar/ 36 Ar ratio of atmospheric Ar, assuming that this ratio has remained constant over hundreds of millions of years and the only nonradiogenic Ar in the unknown is due to atmospheric absorption at current isotopic abundance ratios.

7 177 Actually, Ar isotopes are also produced by several interfering reactions caused by interactions of samples. Therefore, a series of corrections must be made that are especially important for apparently young samples (~10 6 years) and those having a Detailed discussions of these corrections have been (1971), Dalrymple and Lanphere (1971), and Tetley, Z Ar 36 Cl 35 Ca K The most important interfering reactions are those involving the isotopes of Ca. As listed in Table 1, Ca isotopes produce every one of the Ar Mensing (2005). These reactions interfere with the atmospheric Ar correction, which is based on 36 Ar. It is claimed that the abundance of 37 Ar in an Ca interference, but this is not necessarily so if the production cross-sections for 37 different from those for 36 Ar or 37 Ar is radioactive and decays to stable 37 Cl with a short half-life of 35.1 days. Thus a correction for the decay of 37 Ar after irradiation must be made because the Ca abundance derived from 37 Ar is used to N Mass number Stable/unstable Fig. 2. Segment of the chart of the nuclides showing most Cl that participate in nuclear reactions with neutrons Table 1. Interfering nuclear reactions caused by neutron irradiation of mineral samples (after Brereton 1970). Argon Produced Calcium Potassium Argon Chlorine 36 Ar Ca (n, n) 37 Ar Ca (n, ) K (n,nd) 36 Ar (n, ) 38 Ar 42 Ca (n, n) K (n,d) Ar (n, nd, - 37 Cl (n,, - ) 41 K (n,, - ) Ar 42 Ca (n, ) K (n, p) a 38 Ar (n, ) 43 Ca (n, n) K (n, d) Ar (n, d, - Ar 43 Ca (n, ) K (n, p) 44 Ca (n, n) 41 K (n, d) a This is the principal reaction on which the Ar*/ Ar method is based. estimate the contributions to Ar. And Ar is also produced by Ca isotopes. Thus Brereton (1970) derived an equation that relates the age of an irradiated sample to its Ar*/ Ar ratio corrected for and Lanphere (1971) reported their measurements in a reactor to derive correction factors for Ca- and F in equation 12 above. However, there is not enough detail in how their measurements were made to assess their relevance to determining the amount of Ar in the unknown due to radioactive decay. It should be abundantly clear that both these dating techniques are dependent on knowing accurately the rate of respect in which the Ar-Ar dating technique is held by the geochronology community because it is claimed to provide such precise results, it is not independent determination of the total half-life of total Ar*/ Ar ratio used in the age equation 11 above. And second, the the samples of unknown age have sometimes been of course depends on accurately knowing the decay rate. So it is the determinations of the that this methodology is still subject to the eight assumptions listed above. Determination Methods Two approaches have been followed to determine the total decay constant and half-life of long-lived radioactive Direct counting Because of the branched decay of total decay rate has to be determined. Thus there have of is counted in a source material, and divided by the total number of radioactive isotopic abundance of knowledge of the isotopic composition of the parent factors (Begemann et al. 2001).

8 178 A. A. Snelling of, resulting from the electron capture decay mode, is measured in the relevant energy spectrum is determined, which is then divided by the total number of radioactive isotopic abundance of are the geometry and absorption properties of the detection assembly used, how the internal and scatter events are reduced and accounted for, how well the Compton interaction is calculated, and how narrow the energy peak is from which the number 1965). It is estimated that the accuracy of the Leutz, Schulz, and Wenninger (1965), McNair, Glover and Wilson (1956), Saha and Gupta (1960), Sawyer and Wiedenbeck (1950), Spiers (1950), and Suttle and Libby (1955). And many of these and and measurement instrumentation. Several also attempted to measure the electron capture component of the and Wiedenbeck (1950), and Leutz, Schulz, and were measured with the corrections of the counting rates for Tl contents, background, and dead time Leutz, Schulz, and Wenninger (1965) also measured Tl-doped caesium iodide (CsI) crystals. The counting equipment used has included counting tubes or beta Geiger-Müller tubes or counters (Bramley and Sanjeevaiah an ionization chamber (Burch 1953), a proportional counter (McNair, Glover, and Wilson 1956), and Gupta 1960), and liquid scintillation counters After Gopal, Sanjeevaiah, and Sanjeevaiah in 1972 used a Geiger-Müller counter in their direct of 30 years until the most recent direct counting methodology. However, Grau Malonda and Grau and a calibrated solution of several other nuclides in 1 M hydrochloric acid (HCl) was measured in a liquid-scintillation spectrometer to verify the prepared seven amounts of potassium gel to 0.2 mg/l solutions of 3 ) in water. Additionally, to evaluate the background counting rate for each of the seven samples of was added to four other samples of potassium gel to produce unquenched blanks, to which were added increasing amounts of carbon tetrachloride (CCl ) to achieve a chemical quenching equivalent to the a liquid scintillation counter (spectrometer). The seven samples of into the previously measured four-point quench curve (from the four blanks) versus the background seven of in capture -ray component determined from counting 3 H (tritium), to calculate the total prepared four aqueous solutions each of potassium 3, % purity) and potassium 2 g of salt per 10 g of water. To measure background counting rates, four similar solutions were prepared 3 ) and sodium chloride (NaCl) respectively instead of the potassium salts. To avoid errors in the weighing procedure due to hygroscopic behaviour of the salts, two samples were prepared with oven dried salts. Weighed portions of these 16 solutions were variously added to three different scintillators. The sample counting rates varied between 230 and 660 cpm, while all background counting rates were lower than 50 cpm. This means that the random error in the measurements had to vary from 6.6% to 3.9% at least simply due to counting statistics. The total counting time for potassium and background samples was more than 60 days, during which the counting rates of

9 179 all samples were stable. The results of the dried salts agreed perfectly with results obtained with undried salts. The total contribution of the electron capture -ray component the tracer 3 H (tritium). The individual uncertainty contributions to the calculated total also meticulously determined and compared between 3 of the solutions (weighing), preparation of the samples (weighing), purity of the salts, the statistics, and adsorption), impurities of other radioisotopes, ratio), atomic and nuclear data, quench indicator measurement (long periods), non-representative background measurement, and isotopic abundance. The quadratic sum of the uncertainty contributions was 0.23% for the total 3 small for liquid scintillation counting. The higher value half-life value was obtained by averaging the four 3, but the measurements perfectly with the total uncertainty contributions stem from the isotopic abundance of uncertainty contributions from the quenching curves 3 Judged from the fact that many of the earlier are not compatible with one another within the stated uncertainties, it would appear that not all the measurement uncertainties may have been accounted for, and therefore the stated uncertainties may be unrealistically small. According to Begemann et al. by unrecognized systematic errors. As the nature of these errors is obscure, it is not straightforward to true value, although the independent Grau Malonda the presence of unknown systematic biases makes any averaging of them all dangerous. It is possible that reliable results of careful workers, listing realistic uncertainties, will not be given the weights they deserve this aside from the question of whether it makes sense to average numbers that by far do not agree within the stated uncertainties. In any case, there is a natural tendency for bias towards the most recent measurements as though the more modern equipment and methodologies (using computers, for instance) guarantee better results, when in fact intimately involved and careful with their equipment than relying on computers. Also, the fact that the most recent attempts to calibrate the total life value used in geochronology have not relied on viewed as potentially not being well planned. Geological comparisons of methods The second approach to the determination of the total decay constant (and half-life) of date geological samples whose ages have also been measured by other radioisotope dating methods with presumably more reliable decay constants (Dickin in the case of geochronologists because of the large uncertainty contributions in direct counting total life determinations from the isotopic abundance of and the approach essentially involves circular reasoning, because it is being assumed the other radioisotope give the reliable dates to which the total radioisotope ages into agreement. It should be noted, however, that this is hardly objective, because all the radioisotope ages of rocks could be wrong due to the underlying unprovable and suspect assumptions on which all the radioisotope methods are based. Nevertheless, this approach was used as early as It would thus seem that most geologists have come to accept radioisotope dating as factual and therefore the only task left is to reconcile all of the methods into a coherent deep time picture of the solar system. Apart from Renne et al. (1997) who crosscalibrated their Ar-Ar date for the pumice from the AD 79 Vesuvius eruption with that historic date, and ages for Ar-Ar dating standards with the recognized all the other geological comparisons have been with evaluated the geological comparisons together with the most recent direct counting determinations.

10 180 A. A. Snelling This geological comparisons approach has the disadvantage that it involves the geological uncertainties, such as whether all radioisotopic systems closed at the same time and remained closed. However, it is claimed to still provide a useful check on the laboratory determinations by direct physical counting. Nevertheless, this approach entails multi-chronometric dating of minerals and components in individual rocks and meteorites and cross-calibration of different radioisotopic age systems by adjusting the decay constant of the obtained via another radioisotope dating system, because the half-life of U is claimed to be the most accurately known of all relevant radionuclides, this half-life of U. Results of the Potassium- Decay Determinations of the total decay constant and half-life of been made using these two methods. The results are listed with details in Table 2. The year of the determination versus the value of the total points plotted have been color-coded the same to differentiate the values as determined by the three approaches that have been used direct counting, geological comparisons with other radioisotope dating methods, and a combination of these. Discussion The early determinations Ar- Ar (Merrihue and Turner 1966) dating methods are among the most widely applicable in terms of the branched decay of Ca and Ar, two decay constants are relevant to the system. The values of these two decay constants in virtually universal use when Begemann et al. (2001) were calling for improved decay constants for geochronology, namely, -10 yr yr -1 respectively, were those recommended by Steiger and Jäger (1977). Those values are based on and activity respectively) for Gale (1969), updated to include (mean %) by Garner et al. (1975). Beckinsale and Gale (1969) also included an estimated value -2 dps/g for a hypothetical -less decay of Ar. The total constant recommended by Steiger and Jäger (1977) of -10 yr -1 corresponds to a half-life of 1.25 Byr. A later compilation of proportion of available data published before 1969, activity data between 1969 and 2002 do not seem to good addition to an undergraduate laboratory with Direct counting Geological comparisons Combination Half-life (Byr) Year of Determination Fig. 3. method of its determination. The error bars for each determination are also plotted from the error values listed in Table 2.

11 181 Table 2. Determinations of the Year Half-Life (Byr) Uncertainty (Byr) Method Instrument/Procedure Source(s) ±0.3 Direct Counting Geiger-Müller Counter Bramley and Brewer (1938) ±0.2 Direct Counting Beta Counter Borst and Floyd (1948) ±0.15 Direct Counting Beta Counter Gräf (1948a, b) ±0.19 Direct Counting Geiger-Müller Counter ±0.6 Direct Counting Beta Counter Floyd and Borst (1949) ±0.07 Direct Counting Geiger-Müller Counter Gräf (1950) ±0.08 Direct Counting Beta Counter Houtermans et al. (1950) ±0.05 Direct Counting Beta Counter Sawyer and Wiedenbeck (1950) ±0.2 Direct Counting Geiger-Müller Counter Smaller, May, and Freedman (1950) ±0.05 Direct Counting Beta Counter Good (1951) ±0.04 Direct Counting Ionization Chamber Burch (1953) ±0.04 Direct Counting Geiger-Müller Counter Suttle and Libby (1955) ±0.02 Direct Counting Proportional Counter McNair, Glover, and Wilson (1956) ±0.03 Direct Counting Scintillation Spectrometer Kelly, Beard, and Peters (1959) ±0.08 Direct Counting Scintillation Spectrometer Saha and Gupta (1960) ±0.015 Direct Counting Liquid Scintillation Counter Glendenin (1961) Geological Comparisons Smith (1964) ±0.007 Direct Counting Scintillation Spectrometer Leutz, Schulz and Wenninger (1965) ±0.002 Direct Counting ±0.055 Direct Counting Weighted Mean of Previous Determinations ±0.08 Direct Counting Geiger-Müller Counter ±0.08 Direct Counting Direct Counting ±0.08 Direct Counting Geological Comparisons Geological Comparisons Direct Counting ±0.013 Geological Comparisons Adjusted Beckinsale and Gale 1967 Value Adjusted Beckinsale and Gale 1967 Value Repeated Reporting in Nuclear Physics Literature Calibration against the 79AD Vesuvius eruption monitor standards Re-evaluation of Activities Determinations Calibration of ages for a rock unit and a meteorite ±0.004 Direct Counting Liquid Scintillation Counter ±0.004 Geological Comparisons units Beckinsale and Gale (1969) Venkataramaiah, Sanjeevaiah, and Sanjeevaiah (1971) Gopal, Sanjeevaiah, and Sanjeevaiah (1972) Endt and Van der Leun (1973) Steiger and Jäger (1977) Audi et al. (1997) Renne et al. (1997) Renne et al. (1998) Min et al. (2000b) Min et al. (2000a); Renne (2000) Grau Mahonda and Grau Carles (2002) Kwon et al. (2002) ±0.003 Direct Counting Liquid Scintillation Counter Kossert and Günther (2004) ± ± ± Geological Comparisons Geological Comparisons Combination of Re-evaluation of Direct Counting and Geological Comparisons Combination of Re-evaluation of Direct Counting and Geological Comparisons Adopted Kwon et al value to recalibrate mineral Ar-Ar ages Calibration using disparities in ages for rocks and meteorites Calibration of U-Pb and Ar- standards Revision of Renne et al value without LSC data Krumei et al. (2006) Renne et al. (2010) Renne et al. (2011)

12 182 A. A. Snelling limited resources, while the impressively precise Terrani (1977) lists only the standard deviation between different determinations which does geometry factors, chemical purity, etc. In fairness, Begemann et al. (2001) claim that many of the previous studies utilized by Beckinsale and Gale (1969) also failed to quantify potential systematic Leun (1973) used more appropriate statistical methods than Beckinsale and Gale (1969), and the resulting uncertainties for the total activity are much larger. The lower total activity combined with the use of a larger value for the -10 yr -1 (corresponding to a total decay half-life of Byr) for (1977). The data of Garner et al. (1975) for the isotope abundance of was the hypothetical -less electron capture decay. The more recent summary of Audi et al. (1997) reported the same total decay -10 yr -1 (total decay half-life of Byr) as previously cited in the nuclear physics literature, but with a different branching ratio of / + and a The implicit reevaluation of activity data was not discussed by Audi et al. (1997). Begemann et al. (2001) noted that outstanding problems remaining to be addressed in evaluating the better data for and -less electron capture decay directly to Ar in the ground state. and Van der Leun (1973) compilation of activity data with other modern values of physical constants yields a total -10 yr -1 et al. (2000a) also graphically illustrated how the use of different total by tens of millions of years for rocks supposedly more Renne (2000) showed that certain unshocked and rapidly cooled meteorites (acapulcoites) yield Ar- Ar ages indistinguishable from ages determined with other radioisotope systems. The use and calibration of Ar-Ar standards In the Ar- Ar method, which has now largely Age Difference (Ma) Audi et al (1997) Corrected Endt and Van der Leun (1973) Corrected Steiger and Jäger (1977) Age (Ma) based on Steiger and Jäger (1977) Fig. 4. calculated from the decay constants of Audi et el. (1997) the traditional age based on the decay constant of Steiger and Jäger (1977) (corrected), after Min et al. (2000a). constant is needed provided the absolute ages of the Ar- Ar standards (neutron monitors) are known the effects of the standards (see detailed discussion by Min et al. 2000a). Active programs have been underway now for more than a decade to improve the accuracy of both the total the Ar- Ar standards, including development of appropriate statistical methods for their simultaneous determination from geological comparison data (Min et al. 2000b). Thus many attempts have been made to determine more accurately the absolute ages Ar- particular focus in many of these studies has been southwestern Colorado. The methods used to determine and calibrate Ar-Ar ages of the sanidine, plagioclase, hornblende, of other standards of sanidine, plagioclase, biotite, muscovite, and hornblende analyzed concurrently Sr ages of sanidine, plagioclase, and biotite from

13 183 intercalated in the astronomically tuned marine succession of the Melilla Basin in Morocco. Space here precludes detailed discussion of the objectivity of, and assumptions implicit in, these determinations and calibrations. However, in summary it must be emphasized that none of these calibrations is truly independent and thus objective due to the interwoven circular reasoning between all methods by which one method is calibrated against another and then that method is used to calibrate the original method, or another method which is then used to calibrate the original method. And all assumptions involved assumption is that presently measured process rates into the remote past. The usual rejoinder is that multiple radioisotope methods used on the same rocks and meteorites, and minerals from them, yield identical ages so the methods must work, which of course is the rationale for such calibration studies. However, failures of each of the radioisotope dating methods because of inheritance and contamination, contrary to two of the three underlying assumptions involved Snelling (2005) have studied and reported numerous ages between the radioisotope dating methods due to past accelerated radioisotope decay rates, and Snelling (2015c) has demonstrated that meteorite ages determined by the many different radioisotope methods have been calibrated against, to bring ages. Nevertheless, the increasing popularity of the astronomical tuning method is based on its presumed independence of the radioisotope dating methods and the assumption that the orbital motions of the uniformly because the earth is billions of years old and has to have been stable in such orbital behavior through much of that time. In other words, the billions of years are assumed so then the method can calibrate the rocks deposited during millions of years. However, even the astronomical tuning method is calibrated against the radioisotope dating methods. tephra layers intercalated in the marine succession tuned marine succession was used to revise the tuning of this marine succession in Morocco had already been calibrated against the astronomical tuning of the composite sedimentary succession in the Sorbas and Nijar Basins in Spain, which in turn was calibrated against the geomagnetic polarity timescale. However, the geomagnetic timescale itself has been established and calibrated rocks, particularly volcanic rocks, which contain the geomagnetic polarity time intervals and which 2012). Thus this lengthy chain of reasoning begins geomagnetic polarity timescale, and ends with the astronomically tuned marine succession calibrated by the geomagnetic polarity timescale being used to calibrate the Ar-Ar ages of the tephra layers, and the In other words, because there is no objective standard the Ar-Ar method is calibrated against itself! And the astronomical tuning or astrochronology method is not independent of radioisotope dating, as clearly documented by Hinnov and Hilgen (2012). The branching ratio It is claimed that there are two parameters for which accurate values are not needed in the Ar-Ar radioisotope dating method, namely, the branching ratio of composition of, natural potassium (Renne et al. the branching ratio for in natural potassium need to be known in order to determine the total The branching ratio attempts to quantify how much Ar compared Ceccarelli, Quareni and Rostagni (1950), and Sawyer and Wiedenbeck (1950) used Geiger-Müller counters respectively decaying via electron capture to Ar Ca. (1950), and Spiers (1950) used scintillation counters by known added amount of

14 184 A. A. Snelling as Inghram et al. (1950), Mousuf (1952), and Russell et al. (1953) used mass spectrometers to analyse for the Ar and Ca derived from of known age, as determined by their provenance 2 ). Russell et al. (1953) branching ratio to Ar values from <0.7 to 1.9, the to 0.15, and the measurements by others of the Ar branching ratio to Ar values from 0.02 to Beckinsale and Gale (1969) reviewed all the early decay in order to determine the best estimates for the branching ratio, as well as the total Gale (1969) from their analysis of all the then concluded that from the direct measurements with the smallest stated errors of the ratio between the Subsequently, Steiger and Jäger (1977) made no recommendation for the value of the branching ratio but merely implied acceptance of the Beckinsale claiming a branching ratio of Nägler and Villa (2000) utilized an entirely different approach to determine the branching ratio. They successfully attempted both Ca and Ar- Ar dating of the same samples of muscovite from an unsheared pegmatite intruded into a South African Archaean greenstone belt, and of sanidine determined the amounts of radiogenic Ar and Ca derived from the muscovite and sanidine samples by the normal Ar- Ar dating procedure, and by using a double Ca- Ca double spike added to the total Ca separated from the samples, respectively. Then using those amounts they calculated a branching ratio for weighted average of the direct measurements with the smallest stated errors of the ratio between the Villa (2000) value has a halved uncertainty. And it der Leun (1973) value. Interestingly, subsequent efforts to determine the total this work by Nägler and Villa (2000). Instead, Grau Malonda and Grau Carles (2002), adopted a al. (2010) adopted a branching ratio value of et al. (2000a), likewise calculated from the individual decay constants for Ar via electron capture versus to comments from Schwarz et al. (2011), Renne et al. (2011) adjusted their estimate of the branching ratio to by ignoring the liquid scintillation counting determinations of the decay constants by major sources of uncertainty in determinations of the total (2010, 2011) agreed and suggested the uncertainty to calibrate the total using mineral standards and rocks of known ages, as determined by other radioisotope dating methods, Isotopic composition of potassium The other major source of uncertainty in determinations of the total value for the Renne et al. (2010) estimated that uncertainty as the Subsequently Burnett, Lippolt, and Wasserburg (1966) used multiple mass spectrometry analyses of three terrestrial samples (two mineral samples and and two eucrites) to determine whether there was any variation in their found that the the three terrestrial samples between and %, while the Beckinsale and Gale (1969) adopted a determinations more recent than that by Nier (1950) (1967). However, Garner et al. (1975) subsequently

15 185 analyzed the newly produced NIST standard the value then adopted by Steiger and Jäger (1977), (1997) adopted a perhaps a rounding up of the Garner et al. (1975) Laeter et al. (2003) similarly adopted a value of (1) % due to its adoption by the International Union ratio of %, and Renne et al. (2010) a value (1975). Thus to this day the Garner et al. (1975) value is the value for the terrestrial Concern about the level at which the abundance ratio might vary was heightened as a result of Verbeek and Schreiner (1967) reporting few centimeters of potassium-metasomatized granitic contact rocks in South Africa. However, that concern over isotopic fractionation was greatly reduced, at least for terrestrial samples, by the measurements of Humayun and Clayton (1995) which indicated the terrestrial materials at the 0.5% level and thus a near constancy in the Begemann et al. (2001) stated that variations in the relative abundance of that determined by Humayun and Clayton (1995), although they considered it important to emphasize that the Humayun and Clayton (1995) study had absolute value of the Nevertheless, the geochronology community has continued its efforts to reduce the uncertainties in down to around 0.1%. Thus Naumenko et al. (2013) obtained high precision ionization mass spectrometry (TIMS) by three different measurement protocols for the two standard latter being the same standard reference material analyzed by Garner et al. (1975). As a result, they obtained a adopted since 1975 (De Laeter et al. 2003), but with Their value corresponds to a commented that this now reduced the uncertainty in the abundance of with an absolute uncertainty of 0.1% there have to be further improvements in the determination of the total The most recent K half-life determinations So we need to return to the most recent determinations of the total dating methods depend on accurately knowing those values, as well as the electron capture/positron branching ratio. The only two recent direct counting determinations are those performed by Grau Malonda already in detail above. Unlike most previous direct of they obtained essentially the same results, total Renne et al. (2010) initially included the Grau reassessment of the total data and pairs of U- 206 Ar- Ar data for standards, to calibrate the total Ar dating standard. They obtained a half-life value of pointed out that liquid scintillation counting data have a sensitive dependence for the determination of the total - -decay to Ca and electron capture to Ar, the latter including both possible decays (electron capture to the ground - radiation, and the equation(s) governing (2011) noted that while those two liquid scintillation different values for the branching ratio without justifying their choices. Consequently, Renne et al. (2011) revised their Renne et al. (2010) determination of the total by discounting that liquid scintillation counting data.